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In this paper a new criterion for fracture investigation of orthotropic materials with cracks under mixed mode I/II loading is presented. In this fracture criterion, orthotropic material will be considered as a reinforced isotropic material. It is supposed that the crack will grow in the matrix of the orthotropic material. A new definition named here as “isotropic-orthotropic stress reduction factor” (IO-SRF) is utilized to consider the effects of the fracture process zone by a macro-mechanics approach. Also, the stress reduction factors will present a valuable relationship between the orthotropic and isotropic fracture toughness. Experimental and finite element methods will be introduced for computing the stress reduction factors. The SRFs are calculated for samples of glass-epoxy as an orthotropic material and samples of epoxy as a related isotropic one. Experimental tests under mixed mode I/II are performed on glass-epoxy composite samples to evaluate the validity of the presented mixed mode fracture criterion. The results of experimental tests on composite samples show a good agreement with the results of the presented criterion. Thus, the proposed criterion could be utilized as an efficient criterion for investigating the fracture of orthotropic materials under mixed mode I/II loading. [ABSTRACT FROM AUTHOR]

For composite materials, two quantities that are useful for characterizing the contribution of inhomogeneities in a matrix material to the overall properties are (1) the individual H-tensor, H, which describes the contribution of a single inhomogeneity and (2) the overall strain concentration tensor, which describes the relationship between the overall volumetric strain to the average strain of all of the inhomogeneities. In this paper, we develop a relationship expressing the overall H-tensor, $${\mathcal{H}}$$ , in terms of the overall strain concentration tensor. An important feature of the derivation is that it allows for rigorous upper and lower bounds on the overall H-tensor. In the special case that the inhomogeneities are all the same, with the same orientation, then $${\mathcal{H} = {\bf H}_i}$$ , and the results derived for $${\mathcal{H}}$$ also hold for H. [ABSTRACT FROM AUTHOR]

The long-term performance of engineering structures is typically discussed in terms of such concepts as structural integrity, durability, damage tolerance, fracture toughness, etc. These familiar concepts are usually addressed by considering balance equations, crack growth relationships, constitutive equations with constant material properties, and constant or cyclically applied load conditions. The loading histories are represented by changing stress (or strain) states only. For many situations, especially for those associated with high-performance engineering structures, the local state of the material may also change during service, so that the properties used in the equations are functions of time and history of applied conditions. For example, the local values of stiffness, strength, and conductivity are altered by material degradation to create "property fields" that replace the global constants, and introduce time and history into the governing equations. The present paper will examine a small set of such problems, which involve the accumulation of distributed damage and the development of an eventual fracture path leading to failure. Specifically, the paper discusses this problem in the context of material state changes measured by impedance variations as a method of following the details of fracture path development. An analysis and interpretations of observations will be presented, and limitations and opportunities associated with this general concept will be discussed. [ABSTRACT FROM AUTHOR]

In this paper, an accurate formula for calculating the thermal residual stress field in a particle-reinforced composite are presented. Numerical examples are given to show r-variations of the thermal residual stresses. The increase in fracture toughness of matrix predicted by the thermal residual stress field is compared well with the experimentally measured increase. [ABSTRACT FROM AUTHOR]

A new interaction integral formulation is developed for evaluating the elastic T-stress for mixed-mode crack problems with arbitrarily oriented straight or curved cracks in orthotropic nonhomogeneous materials. The development includes both the Lekhnitskii and Stroh formalisms. The former is physical and relatively simple, and the latter is mathematically elegant. The gradation of orthotropic material properties is integrated into the element stiffness matrix using a ``generalized isoparametric formulation'' and (special) graded elements. The specific types of material gradation considered include exponential and hyperbolic-tangent functions, but micromechanics models can also be considered within the scope of the present formulation. This paper investigates several fracture problems to validate the proposed method and also provides numerical solutions, which can be used as benchmark results (e.g. investigation of fracture specimens). The accuracy of results is verified by comparison with analytical solutions. [ABSTRACT FROM AUTHOR]

The paper addresses the well-known (from available publications) phenomenological strength criteria for anisotropic materials, which are most widely used in application software. [ABSTRACT FROM AUTHOR]

Abstract  The symmetric-Galerkin boundary element method (SGBEM) has previously been employed to model 2-D crack growth in particulate composites under quasi-static loading conditions. In this paper, an initial attempt is made in extending the simulation technique to analyze the interaction between a growing crack and clusters of perfectly bonded particles in a brittle matrix under cyclic loading conditions. To this end, linear elastic fracture mechanics and no hysteresis are assumed. Of particular interest is the role clusters of inclusions play on the fatigue life of particulate composites. The simulations employ a fatigue crack growth prediction tool based upon the SGBEM for multiregions, a modified quarter-point crack-tip element, the displacement correlation technique for evaluating stress intensity factors, a Paris law for fatigue crack growth rates, and the maximum principal stress criterion for crack-growth direction. The numerical results suggest that this fatigue crack growth prediction tool is as robust as the quasi-static crack growth prediction tool previously developed. The simulations also show a complex interplay between a propagating crack and an inclusion cluster of different densities when it comes to predicting the fatigue life of particulate composites with various volume fractions. [ABSTRACT FROM AUTHOR]

The fracture process of composite laminates subjected to static or fatigue tensile loading involves sequential accumulation of intra- and interlaminar damage, in the form of transverse cracking, splitting and delamination, prior to catastrophic failure. Matrix cracking parallel to the fibres in the off-axis plies is the first damage mode observed. Since a damaged lamina within the laminate retains certain amount of its load-carrying capacity, it is important to predict accurately the stiffness properties of the laminate as a function of damage as well as progression of damage with the strain state. In this paper, theoretical modelling of matrix cracking in the off-axis plies of unbalanced symmetric composite laminates subjected to in-plane tensile loading is presented and discussed. A 2-D shear-lag analysis is used to determine ply stresses in a representative segment and the equivalent laminate concept is applied to derive expressions for Mode I, Mode II and the total strain energy release rate associated with off-axis ply cracking. Dependence of the degraded stiffness properties and strain energy release rates on the crack density and ply orientation angle is examined for glass/epoxy laminates. Suitability of a mixed mode fracture criterion to predict the cracking onset strain is also discussed. [ABSTRACT FROM AUTHOR]

For the better use of composites and a deeper insight into the fracture propagation and stress transfer of the interface between fiber and matrix, a theoretical solution of closed form is presented with the assumed bilinear local bond-slip law and a parabolic shear stress distribution along the thickness of the matrix. The load-displacement relationship and interfacial shear stress are obtained for four loading stages. Finally, the effects of Young's modulus of fiber (matrix) and bond length on the performance of the interface are illustrated. [ABSTRACT FROM AUTHOR]

Abstract: This work established a new analytical model based upon the equivalent constraint model (ECM) to constitute an available predictive approach for analyzing the ultimate strength and simulating the stress/strain response of general symmetric laminates subjected to combined loading, by taking into account the effect of matrix cracking. The ECM was adopted to mainly predict the in-plane stiffness reduction of the damaged laminate. Basic consideration that progressive matrix cracking provokes a re-distribution of the stress fields on each lamina within laminates, which greatly deteriorates the stress distributed in the primary load-bearing lamina and leads to the final failure of the laminates, is introduced for the construction of the failure criterion. The effects of lamina properties, lay-up configurations and loading conditions on the behaviors of the laminates were examined in this paper. A comparison of numerical results obtained from the established model and other existed models and published experimental data was presented for different material systems. The theory predictions demonstrated great match with the experimental observations investigated in this study. [Copyright &y& Elsevier]

The purpose of this study is to propose a method to correlate micro-structural characteristics of two-phase steel with structural performance in terms of ductile crack growth resistance (R-curve). For this purpose, a meso-scopic simulation method is proposed to predict two types of ductile properties of two-phase steel that control the R-curve from micro-structural characteristics. The R-curve of three-point bend specimen with fatigue pre-crack predicted by a macro-scopic simulation method that we have proposed, in which these two types of ductile properties obtained by the proposed meso-scopic methods are implemented, is in good agreement with experimental result. [ABSTRACT FROM AUTHOR]

A crack in a composite wedge consisting of two dissimilar anisotropic materials under concentrated antiplane loads is analyzed. The problem of a crack in an isotropic composite wedge is solved first by using the Mellin transform and the Wiener-Hopf method. Using a linear transformation of the original composite wedge into an isotropic composite wedge consisting of dissimilar isotropic materials, the antiplane displacement and stresses for the anisotropic composite wedge are obtained from the solution for the transformed wedge. The stress intensity factor for the crack in the original anisotropic composite wedge is obtained from the solution of the crack in the transformed wedge. Special attention is given to the asymptotic problem of a wedge crack in an anisotropic bimaterial. Numerical computations are carried out to obtain the energy release rate for various apex angles and anisotropic parameters as a function of crack angle. [ABSTRACT FROM AUTHOR]

model is developed to analyze the growth of a fiber/matrix debond along a broken fiber interface in a single-fiber composite subjected to tension-tension fatigue. The Paris law expressed in terms of debond growth and strain energy release rates is used. An analytical solution for the Mode II energy release rate G is obtained for long debonds, where the interface crack growth is self-similar. For short debonds, the interface crack interacts with the fiber break, and therefore a FEM modeling in combination with the virtual crack closure technique was performed to calculate the increase in G . Finally, the calculated G dependences are summarized in simple expressions that are used to simulate the debond growth in fatigue. A parametric study of the effect of Paris law parameters on the debond growth is performed. [ABSTRACT FROM AUTHOR]

bimaterial containing an interface crack and consisting of a homogeneous material and a functionally graded material (FGM) with a system of small internal cracks is considered. The thermal fracture of the biomaterial under the action of a heat flux applied to it at infinity is investigated. The problem is studied in the case where the interface crack is much larger than the internal ones. It is assumed that the thermal properties of the FGM are continuous functions of the thickness coordinate. Asymptotic analytical formulas for the thermal stress intensity factors (TSIFs) at the tips of the interface crack are obtained as series in a small parameter (the ratio between sizes of the internal and interface cracks). Then, the critical heat fluxes and the angles of propagation direction of the interface crack are calculated using the criterion of maximum circumferential stress. A parametric analysis shows that the propagation direction of the interface crack depends on the location and orientation of the system of internal cracks. The parameters of inhomogeneity of the FGM affect the value of TSIFs and, hence, the deflection angle of the interface crack. [ABSTRACT FROM AUTHOR]

We explore the compliance approach for K I evaluation of a cracked three point beam (TPB) of functionally graded material (FGM). We suggest an equivalent beam of variable height for cracked FGM beams which includes the homogeneous beam for the linear, quadratic and cubic variations in elastic modulus along the beam span. The efficacy of equivalent beams is demonstrated numerically on a 250 × 41 × 6 mm FGM beam with modulus varying from 210 – 315 GPa under 5000 N load. [ABSTRACT FROM AUTHOR]

The prestressed end-notched flexure fracture specimen is developed in the present work, which combines the traditional double-cantilever beam and the end-notched flexure specimens in a very simple way. The most important features of the new beam-like specimen are that it is able to provide any combination of the modes I and II strain energy release rates and it may be performed by using a simple three-point bending fixture. The mode-I part of the strain energy release rate is fixed by inserting a steel roller, which causes a fixed crack opening displacement. The mode-II part of the energy release rate is provided by the external load. A simple closed-form solution using beam theory is developed for the energy release rates of the new configuration. The applicability and the limitations of the novel configuration are demonstrated using unidirectional glass/polyester composite specimens. If only propagation onset is involved then the prestressed end-notched flexure specimen can be used to obtain the fracture criterion of transparent composite materials in a very simple way. [ABSTRACT FROM AUTHOR]

A two-level fracture model of composites with cracks under compression is proposed. Fiber-reinforced laminated panels with a hole are considered. The panels are compressed along the fibers so that two cracks propagate from the hole boundary at a right angle to the loading direction. The fracture mechanism is analyzed at two levels. The first level is the compression-induced stress concentration at the tip of a finite-thickness crack filled with a fractured material. At this level, the theory of elasticity of linear orthotropic body is used. The second level is compression fracture at the crack tip. The analysis performed at this level involves the three-dimensional linearized theory of stability of solids, considering microcracks in the interface between the fractured and intact materials, and the exact solution describing the compression-induced instability of the cracked interface. The second level is where results obtained by the author are used. Thus, the approach proposed employs the theory of elasticity of linear orthotropic body and the three-dimensional linearized theory of stability of solids to analyze a specific mechanism of fracture [ABSTRACT FROM AUTHOR]

We demonstrate the ability to determine stress intensity factors in orthotropic materials directly from measured temperatures away from the crack and using far-field expressions for the stresses. This is advantageous, recognizing that recorded thermoelastic data can be very unreliable near the tip of a crack. In addition to singular terms that govern in the immediate vicinity of the crack tip, the present series expressions for the stresses contain higher-order finite terms. Little measured input information is needed and data acquisition positions can be selected largely at the user's discretion. [ABSTRACT FROM AUTHOR]

The influence of initial tension or compression along cracks on the stress intensity factor (SIF) at crack tips under the action of additional normal forces on crack edges is studied for infinite bodies. A strip made of a composite material is considered. The strip ends are simply supported, and the strip contains a crack whose edges are parallel to its face planes. The strip is first stretched or compressed along crack edges, and then additional uniformly distributed normal forces are applied to the crack edges. The influence of the initial tension (compression) on the SIF caused by the additional normal forces is studied. The corresponding boundary-value problems are modelled with the use of the three-dimensional linearized theory of elasticity. All the investigations are carried out numerically by employing the finite-element method. The values of SIF are calculated by the energy release method. [ABSTRACT FROM AUTHOR]

Fluorescence microprobe spectroscopy was used in [1] to determine in situ microstress fields that develop during fracture in a model ceramic/metal composite. In particular, experimental and theoretical procedures were described in order to relate the experimental peak-shift to the various stress components and combinations thereof. Based on suitable micromechanical concepts, these stress maps are now used to predict quantities related to the fracture mechanics, such as (critical) stress intensity factors, R-curves, and crack-opening displacements. All predictions are compared with direct measurements of these quantities to demonstrate the feasibility and soundness of the micromechanics approach. [ABSTRACT FROM AUTHOR]

We have studied the effect of residual stresses on fracture resistance and crack arrest behavior of asymmetric ceramic laminated Si3N4/Si3N4-TiN structures. Using the compliance method, we assessed the technique of R-curve construction for laminar composites. For laminar structures with layers varying by their elastic characteristics we developed an analytical method for calculation of "fracture resistance - crack length" dependence. The method applicability is verified by calculation of stress intensity factors for laminar specimens with an edge crack The calculated results are compared to the experimental data. [ABSTRACT FROM AUTHOR]

The effect of static and cyclic loading conditions on the stress corrosion cracking of unidirectional glass reinforced polymer (GRP) rods used in composite high voltage insulator has been investigated. A series of stress corrosion experiments have been performed on unidirectional E-glass/modified polyester composite rods. The rods have been subjected to mechanical tensile static and cyclic stresses in the presence of a nitric acid solution. The stress corrosion fracture process in the rods was monitored using acoustic emission techniques. The experimental loading conditions simulated possible in-service loadis for composite suspension insulators. The results obtained in this study showed that the brittle fracture process can be generated in the rods when subjected to relatively low tensile stresses in the presence of a nitric acid solution. The morphology of the experimentally generated brittle fracture cracks in the rods closely resemble those from in-service failed composite suspension. It has also been shown in this research that low frequency, low amplitude vibrations in tensile loads can significantly accelerate the fracture process. It appears that the brittle fracture cracks in the rods generated under cyclic loads are less planar in nature in comparison with the cracks formed under static conditions. It has also been found that the acoustic emission generated during the stress corrosion fracture process in the rods is sensitive to the placement of the transducers. However, reasonably good correlation between the stress corrosion crack growth rates and acoustic emission has been attained. [ABSTRACT FROM AUTHOR]